X₁, X2,...,xn is a random sample from the population that follows a Poisson distribution with the density function: -0 0x f (x10) = ; x = 1,2,3,.... x! If you want to test Ho: 0 = 3 and Ho 03 at a significance level of a = 5%, determine : 1. Likelihood function L(x: 0) = f(x₁,x₂,...,xn10) and the maximum likelihood estimator for 8 2. The Likelihood function under Ho and H₁, is L(x: 0o = f(x₁,x₂,...,x₂100) and L(x: 0₁) = f(x₁,x₂,...,x₂0₁) 3. Likelihood ratio statistics, namely: -2ln(x: 00,0₁) with L (x: 00) 2(x: 0,0₁) = L (x: 01) 4. test rejection area and give your conclusion if you have statistic Σ1 x = 80
X₁, X2,...,xn is a random sample from the population that follows a Poisson distribution with the density function: -0 0x f (x10) = ; x = 1,2,3,.... x! If you want to test Ho: 0 = 3 and Ho 03 at a significance level of a = 5%, determine : 1. Likelihood function L(x: 0) = f(x₁,x₂,...,xn10) and the maximum likelihood estimator for 8 2. The Likelihood function under Ho and H₁, is L(x: 0o = f(x₁,x₂,...,x₂100) and L(x: 0₁) = f(x₁,x₂,...,x₂0₁) 3. Likelihood ratio statistics, namely: -2ln(x: 00,0₁) with L (x: 00) 2(x: 0,0₁) = L (x: 01) 4. test rejection area and give your conclusion if you have statistic Σ1 x = 80
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please answer number 4
Transcribed Image Text:X₁, X2, Xn
is a random sample from the population that follows
a Poisson distribution with the density function:
-0 0*
f (x10) =
; x = 1,2,3,....
x!
If you want to test Ho: 0 = 3 and Ho 0 # 3 at a significance level
of a = 5%, determine :
1. Likelihood function L(x : 0) = f(x₁, x2, ...., Xñ[0) and the
maximum likelihood estimator for 8
2. The Likelihood function under Ho and H₁, is L(x: 0o =
f(x₁,x2,..., xn100) and L(x: 0₁) = f(x₁,x₂,..., xn|0₁)
3. Likelihood ratio statistics, namely: -2ln(x: 00, 0₁) with
L (x: 00)
2(x: 00, 0₁) =
L (x: 01)
4. test rejection area and give your conclusion if you have statistic
Σ1 x = 80
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